Place onions on grill and cook until beginning to char, turning and brushing often with oil mixture, about 11 minutes. Brush top side of onions with mustard mixture and cook until mixture begins to bubble, about 2 minutes. Turn onions; brush with mustard mixture and grill until beginning to caramelize, about 1 minute longer. Transfer onions to plate. Brush with mustard mixture. Makes 4 to 6 servings.